(i)) While factorizing a given polynomial, using remainder & factor theorem, a student finds that (2x + 1) is a factor of 2x³ + 7x² + 2x - 3.
(a) Is the student's solution correct stating that (2x + 1) is a factor of the given polynomial?
(b) Give a valid reason for your answer.
Also, factorize the given polynomial completely.

(ii) A line segment joining P (2, -3) and Q (0, -1) is cut by the x-axis at the point R. A line AB cuts the y axis at T(0,6) and is perpendicular to PQ at S. Find the:
(a) equation of line PQ
(b) equation of line AB
(c) coordinates of points R and S.

(iii) In the given figure AC is the diameter of the circle with centre O. CD is parallel to BE.
∠AOB = 80° and ∠ACE = 20°. Calculate
(a) ∠BEC
(b) ∠BCD
(c) ∠CED

Solution

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